There are several possible causes of browning needles on your dwarf Alberta spruce (Picea glauca 'Conica'). One is the spruce spider mite. This tiny mite is active during cool fall and spring weather, feeding on needles of the spruce. If you look closely, you may see yellowish stippling on the needles; it results from a toxin injected into the needles from the mites' feeding. If populations are high, you may also see webbing. Often needles turn brown later in summer when temperatures rise. At that point, little can be done for the tree. You can spray with a miticide or horticultural oil when the mites are present in spring or fall to prevent the problem in the future.

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Another possibility is winter damage on that spruce. Evergreens don't go completely dormant, so a dry autumn, drying wind, and dry soil can cause browning. The browned needles won't recover from winter damage, though the tree may produce new growth from buds on browned branches. The new growth may eventually mask the browned area. Water spruces well going into fall and winter to prevent desiccation. Midwinter watering may be needed if conditions remain dry and the soil is not frozen.